Broadband on-chip Half Maxwell Fisheye

Technical Summary: Broadband on-chip Half Maxwell Fisheye

Problem Statement
The miniaturization of photonic components is critical for increasing the integration level and performance of Photonic Integrated Circuits (PICs). Gradient Index (GRIN) optics offers a pathway to this miniaturization by allowing the design of arbitrary index profiles, potentially creating aberration-free lenses. The Maxwell Fish-Eye (MFE) is a historically significant GRIN lens capable of forming perfect images in geometric optics. However, its practical implementation in the optical domain, particularly for telecommunication wavelengths on integrated platforms, remains challenging due to fabrication constraints. While MFE and Half Maxwell Fish-Eye (HMFE) devices have been demonstrated in microwave, terahertz, and some optical regimes using various materials (polymers, ceramics, varying layer thicknesses), a robust, CMOS-compatible implementation for silicon photonics operating in a broadband, non-resonant regime is required.

Methodology
The authors propose and realize a 2D Half Maxwell Fish-Eye (HMFE) on a Silicon On Insulator (SOI) platform for telecommunication wavelengths ($\lambda_0 = 1.55$ $\mu$m).

• Design Strategy: The HMFE is implemented using a Graded Photonic Crystal (GPC). The device operates in the non-resonant metamaterial regime, where the lattice period $a$ is smaller than the Bragg limit ($a < \lambda/2n_{eff}$), ensuring the photonic crystal behaves as a homogeneous, isotropic, and nearly dispersionless medium.
• Index Profile: The required radial refractive index profile, $n(r) = n_0 / [1 + (r/R)^2]$, is achieved by gradually varying the air filling factor ($\eta$) of the hexagonal lattice air holes within the silicon layer. This modifies the effective index ($n_{eff}$) of the guided TE0 mode.
• Simulation: 3D Finite-Difference Time-Domain (FDTD) simulations were conducted to verify the optical properties, specifically the focusing of an incident plane wave.
• Fabrication: The device was fabricated on a 220 nm thick silicon layer (on a 2 $\mu$m SiO2 substrate) using electron beam lithography and Inductively Coupled Plasma (ICP) etching, adhering to CMOS-compatible processes.
• Characterization: Two experimental methods were employed:
  1. Fan-shaped Output Waveguides: A set of 13 output waveguides was used to map the spatial distribution of the output field and determine the focal length by varying the distance ($D$) between the lens rim and the waveguides.
  2. Scanning Near-Field Optical Microscopy (SNOM): An aperture-SNOM system was used to scan the surface of the lens, collecting evanescent waves to generate 2D maps of the electric field intensity ($|E|^2$) and wavefront curvature.

Key Contributions and Results

• Broadband Focusing: The FDTD simulations demonstrated that the HMFE maintains excellent focusing capacity across a broad wavelength range (1450 nm to 1590 nm).
• Experimental Validation:
  • The fan-shaped waveguide characterization confirmed that the output wave is concentrated in the central waveguide when the distance $D=0$ $\mu$m, indicating a focal length at the lens rim. This focusing behavior was observed across the 1380–1640 nm range.
  • SNOM characterization at $\lambda_0 = 1550$ nm provided direct visual evidence of the wavefront curving inside the lens and the subsequent focusing to a bright spot at the rim.
• Quantitative Performance:
  • The Full Width Half Maximum (FWHM) of the focal spot measured via SNOM was 0.466$\lambda_0$ (0.723 $\mu$m) at 1550 nm.
  • This experimental result closely matches the simulated FWHM of 0.403$\lambda_0$ (0.624 $\mu$m).
  • The lens thickness is approximately 3.18$\lambda_0$.
• Fabrication Tolerance: Despite minor fabrication imperfections where the smallest air holes (designed at 46 nm) were etched to approximately 54 nm, the device functionality remained largely unaffected, as these deviations only caused minimal changes to the effective index.

Significance and Claims
The paper claims to provide the first experimental evidence of a broadband, on-chip HMFE for silicon photonics operating in the non-resonant metamaterial regime. The authors assert that their results confirm that Graded Index optics, realized through Graded Photonic Crystals, is a viable and effective approach for miniaturizing components in Photonic Integrated Circuits. The device successfully demonstrates the ability to focus a plane wave incident on its planar surface onto its spherical output surface with high efficiency and broadband performance, validating the theoretical design through both simulation and rigorous experimental characterization. The authors note that due to the non-resonant nature of the operation, the device is expected to remain functional at wavelengths longer than those tested.